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Background:
Systematic Review

Analytical Models to Optimize Tacrolimus Dosing in Solid Organ Transplantation: A Systematic Review

by
Elmira Amooei
1,*,
Nandini Biyani
2,
Amos Buh
2,3,
Martin M. Klamrowski
4,
Nawaf M. Alyahya
5,
Christopher R. McCudden
6,7,
James R. Green
1,
Babak Rashidi
8,
Haya Almuzirai
8,
Stephanie Hoar
9,
Ayub Akbari
2,8,9,
Gregory L. Hundemer
2,8,9 and
Ran Klein
1,10,11,*
1
Department of Systems and Computer Engineering, Carleton University, Ottawa, ON K1S 5B6, Canada
2
Kidney Research Centre, Ottawa Hospital Research Institute, Ottawa, ON K1H 8L6, Canada
3
Faculty of Health Sciences, University of Ottawa, Ottawa, ON K1N 6N5, Canada
4
Department of Mechanical Engineering, University of Ottawa, Ottawa, ON K1N 6N5, Canada
5
Division of Nephrology, Department of Internal Medicine, College of Medicine, Imam Abdurahman Bin Faisal University, Al Khobar 31441, Saudi Arabia
6
Eastern Ontario Regional Laboratory Association, Ottawa, ON K1H 8L6, Canada
7
Division of Biochemistry, Department of Pathology and Laboratory Medicine, University of Ottawa, Ottawa, ON K1N 6N5, Canada
8
Division of General Internal Medicine, Department of Medicine, University of Ottawa, Ottawa, ON K1N 6N5, Canada
9
Division of Nephrology, Department of Medicine, University of Ottawa, Ottawa, ON K1N 6N5, Canada
10
Methodological and Implementation Research Program, Ottawa Hospital Research Institute, University of Ottawa, Ottawa, ON K1N 6N5, Canada
11
Division of Nuclear Medicine, Department of Medicine, University of Ottawa, Ottawa, ON K1N 6N5, Canada
 
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*
Authors to whom correspondence should be addressed.
Pharmaceutics 2026, 18(4), 430; https://doi.org/10.3390/pharmaceutics18040430
Submission received: 10 February 2026 / Revised: 17 March 2026 / Accepted: 28 March 2026 / Published: 31 March 2026
(This article belongs to the Section Physical Pharmacy and Formulation)
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Abstract

Background: Tacrolimus dose optimization remains challenging due to its narrow therapeutic range and multiple influencing variables. This systematic review aimed to identify effective analytical modeling techniques for optimal tacrolimus dose prediction in solid organ transplant recipients. Methods: Two independent researchers conducted a comprehensive review of studies examining analytical models that optimize tacrolimus dosing, searching Medline, Scopus, Embase, Web of Science, and PubMed. Results: In total, 115 studies met the inclusion criteria. Pharmacokinetic models (74 studies), particularly two-compartment with Bayesian forecasting, were most frequently used. Machine learning (ML) approaches, with increasing adoption, have demonstrated promising improved predictive accuracy. Key predictive variables included CYP3A5 genotype, hematocrit levels, post-operative days, and weight; however, the significance of genomic features seemed to diminish progressively as therapeutic drug monitoring calibrates dosing in the months following post-transplant. Only ten studies performed external validation, and none incorporated adherence data or predicted long-term graft outcomes. Conclusions: Clinical deployment of predictive models for tacrolimus dosing remains uncommon. In research, pharmacokinetic models remain prevalent, with ML approaches showing early incremental promise. Limited external validation raises generalizability concerns. Future research should prioritize outcome-based evaluation metrics rather than error metrics.

1. Introduction

Tacrolimus is a calcineurin inhibitor frequently used as an immunosuppressive agent in solid organ transplantation to prevent graft rejection for kidney, liver, pancreas, heart, and lung transplant recipients [1,2]. Tacrolimus has a narrow therapeutic window with serious complications from under- or overdosing [3]. Overdosing can induce significant nephro- and neurotoxicity [4,5], while underdosing may lead to organ rejection [4,6,7]. Optimal dosing is challenging due to complex pharmacokinetics and drug–drug and food–drug interactions [4,5].
Initial dosing is typically patient weight-based, followed by iterative adjustments informed by trough blood concentration measurements. Unfortunately, this approach often fails to reach target concentrations [8], with studies showing that only 37% of kidney transplant recipients achieve target ranges when following the traditional weight-based dosing [8,9]. Target ranges are evidence-based and vary by organ and post-transplant periods. Furthermore, patient responses vary substantially, due to factors including genetics (CYP3A4 and CYP3A5 polymorphism) [10,11,12], demographics [12,13,14], laboratory parameters (albumin, hematocrit, and liver function) [12,15], and various drugs (notably CYP3A inhibitors like fluconazole) [15] and food interactions (e.g., grapefruit) [16,17].
The variability of blood tacrolimus concentration is further exacerbated by complex pharmacokinetics. After oral administration, it is absorbed through the intestines at a rate varying by individual, distributed by binding to erythrocytes and plasma proteins, metabolized through CYP3A enzymes, and excreted mainly through biliary routes [18]. The key pharmacokinetic parameters are defined in Table 1.
While a single-compartment model uses pharmacokinetic parameters to predict future drug concentrations, tacrolimus behavior is often more complex [15]. To address these challenges, researchers have developed more sophisticated models, including multi-compartment models, Bayesian estimation, ML approaches, and statistical models [19,20,21,22]. These models integrate multiple compartments associated with tacrolimus metabolism, storage, and clearance to more accurately model concentrations at arbitrary time intervals [18,21,23,24].
Conversely, trough-level concentrations represent the most simplified tacrolimus pharmacokinetic model, evaluating blood concentrations immediately preceding the next dose (example at 12 or 24 h post dose depending on formulation). Trough levels are relatively easily measured in the outpatient setting. The patient response to tacrolimus can be succinctly summarized as the ratio of trough-level concentrations to prescribed dose (C/D) once sufficient dosing cycles have elapsed to reach a steady state (e.g., after at least 7 days since last dose change).
Despite numerous studies exploring predictive models for tacrolimus dosing, a comprehensive synthesis of modeling approaches is lacking [18,19,21,22,25,26,27,28,29,30]. This systematic review explores the literature on various endpoints, including concentration, trough, and dose prediction studies, beyond the pharmacokinetic modeling methods that are widely investigated. We include ML approaches and summarize the most significant predictors influencing tacrolimus blood concentrations, describe the importance of genomics, and synthesize existing evidence to guide the future development of predictive models as clinical dosing decision aids. Our review is complementary to other reviews, such as the work of Hoffert et al. (2024) [31] and Lloberas et al. (2025) [32], in that we identify a larger corpus of studies incorporating both popPK and ML approaches, and systematically explore endpoints, predictive covariates, and error structures.

2. Materials and Methods

This systematic review followed the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA, Supplementary Material S1) [33] guidelines and was registered with the International Prospective Register of Systematic Reviews (PROSPERO) [34] (CRD42024537212). The protocol was previously published [35].

2.1. Inclusion Criteria

We used PICO (Population, Intervention, Comparison, Outcome) criteria to select the right studies: Population: Adult patients (≥18 years) who underwent solid organ transplantation (e.g., kidney, liver) with analytical tacrolimus dose/concentration prediction models. Intervention: Analytical models or methods (statistical, ML, Bayesian, or kinetic) for tacrolimus dose prediction and/or maintenance of its blood concentration. Comparison: Alternative methods, such as clinician discretion. Outcomes: Significant covariates influencing tacrolimus concentration, and metrics used to evaluate model performance.

2.2. Types of Included Studies

Experimental study designs, including before-and-after studies, cross-sectional studies, cohort studies, qualitative studies, and randomized control trials (RCTs), in English or French, were included regardless of the publication year.

2.3. Search Strategy

Systematic searches were conducted in databases including Ovid/MEDLINE, PubMed/MEDLINE, Scopus, Web of Science, and Embase (1946–11 March 2024) in collaboration with a librarian (RS). Search terms included controlled terms and free-text terms: ‘tacrolimus’, ’dose prediction’, ‘machine learning’, ‘Bayesian theorem’, and ‘kinetic modeling’. Search was limited to human and adult studies. The full search strategy is in Supplementary Material S2. Grey literature was explored through Google Scholar. Conference abstracts published within two years of the search date (published in and after January 2022) were included.

2.4. Study Selection and Eligibility Criteria

Studies were imported into the Covidence software © 2024 [36] for screening. Duplicates were identified through Covidence or through manual screening. Two independent reviewers (EA, MMK) performed title–abstract and full-text screening; disagreements were resolved by a third reviewer (AB). Data extraction was performed using the Joanna Briggs Institute Meta-Analysis of Statistics Assessment and Review instrument [37] (Supplementary Material S3). Four reviewers (EA, NB, MMK, NA) extracted data; discrepancies were resolved by EA.

2.5. Quality of Evidence and Risk-of-Bias Assessment

Evidence quality was assessed using the Grading of Recommendations Assessment, Development and Evaluation (GRADE) [38]. Risk of bias was assessed using the Joanna Briggs Institute (JBI) Critical Appraisal Checklist for Systematic Reviews and Research Syntheses [37] by two independent reviewers (EA, NB). Disagreements were resolved through discussion.

2.6. Data Synthesis

A narrative synthesis was conducted. Only four studies had sufficient data for meta-analyses; due to this limitation, we refrained from conducting a meta-analysis.

3. Results

3.1. Study Characteristics

A total of 115 studies were included for narrative synthesis (Table 2, Figure 1). The predominant focus was on kidney (74 studies) and liver (25 studies) transplant recipients (Figure 2A). Most studies were retrospective in design (101 studies), with only six prospective and four clinical trials (Figure 2B).
Patient cohort sizes varied widely (10–5439 with a median of 66 patients, Figure 2C); as did post-operative follow-up periods, spanning from early post-operative days (0–14 days in 8 studies) to long-term (>1 year in 14 studies), with 41 studies focusing on the first 3 months of the post-transplant period (Figure 2D). Sixty-four studies investigated the immediate-release formulation (Prograf®), followed by the extended-release (Advagraf®, 17 studies) (Figure 2E). Tacrolimus trough whole-blood concentrations were most commonly measured using immunoassays (59 studies, Figure 2F) or mass spectrometry (31 studies). The median male population for model development was 67% (Figure 2G), and 70 studies (75%) had a male-dominant cohort (i.e., ≥60% male population, Figure 2H). The largest number of studies originated from China (28), followed by France (21 studies) (Figure 3).

3.2. Quality Appraisal of Studies

Following JBI critical appraisal guidelines, 99 papers (86%) were scored as a high risk of bias (>60%), mainly due to a failure to provide a clear description of dataset split or patient censoring methods. Moreover, 64 studies (56%) failed to explicitly state the inclusion criteria; however, all studies specified the participants’ characteristics (Supplementary Material S3).

3.3. Prediction Targets

Prediction targets varied amongst the studies, underscoring different clinical objectives for tacrolimus management. These were divided into concentration prediction (to illustrate hourly concentration changes post-dose, for long- and short-term management), trough prediction (to predict the lowest concentration in the blood before next dosing, for long- and short-term management), and dose recommendation. Trough prediction is fundamentally different from (hourly) concentration prediction, as trough prediction captures a single blood sample prediction before the next dose is administered. Concentration prediction, using area under the curve (AUC) calculations, measures the systemic drug exposure over an entire period between two dosing events, which requires multiple blood samples collected at specific timepoints (specific post-dose hours, Figure 4D).
In AUC modeling, the input data should be verified for an accurate dose and collection time, as a sample collection time mismatch could result in substantial shifts in AUC predictions. Trough prediction models are slightly more flexible regarding sampling time mismatch, but do not capture intra-dose variabilities, especially in inpatient and immediate post-transplant populations due to the tacrolimus half-life.
No studies predicted long-term (>1 year) outcomes like graft survival directly. Clinical thresholds for safe or unsafe predictions were explicitly incorporated in 44 studies, typically defining therapeutic blood concentration ranges (e.g., 8–12 ng/mL in early post-transplant, 5–10 ng/mL later).

3.4. Tacrolimus Concentration Prediction

Forty studies predicted 12 or 24 h average tacrolimus blood levels (i.e., between dosing) [13,25,27,28,29,47,52,53,59,60,64,70,75,80,88,97,98,99,102,106,111,113,115,116,117,118,119,120,121,125,126,127,129,130,132,138,139,140,141]. For AUC12 prediction, C2 (concentration at two hours post-dose) was most frequently concluded to be the optimal single-point surrogate (18 studies), followed by C4 (12 studies) [47,60,64,88,99,111,115,118,121,125,126,127,129,138]. Multi-point strategies (C0 + C2 + C4) improved accuracy in eight studies. For AUC24, C2 and C2.5 were strong predictors (10 studies), alongside C0 and C3 [53,70,97,102,116,121,125,141].

3.5. Tacrolimus Trough and Dose Prediction

The next-day trough prediction was modeled in 31 studies. Hybrid targets combining dose recommendation and response prediction were explored in 15 of these studies. Twenty–seven studies focused on the next dose (for different post-transplant periods) [10,12,14,18,21,29,43,55,56,65,66,71,74,81,90,94,96,101,105,108,112,113,134,135] or initial-dose [10,39,44,72,76,93,128] prediction, emphasizing short-term inpatient management.

3.6. Modeling Techniques

Population pharmacokinetic (popPK) models dominated (74 studies), especially using two-compartment models (29 studies) [12,13,18,22,27,39,41,42,44,45,52,55,92,115,118,121,122,124,130,135,141] followed by one-compartment modeling (23 studies, Figure 4B) [29,45,57,61,66,71,78,79,81,82,89,91,92,96,97,98,112,113,115,116,123,127,141,142]. Bayesian estimation was frequently paired with two-compartment popPK models (29 studies), using NONMEM® (58 studies), or Pmetric (12 studies). Gérard et al. developed a 13-compartment physiologically based pharmacokinetic (PBPK) model [76], and Pei et al. used a 15-compartment model [110], representing the most complex structural approaches. All of these models processed longitudinal data over the entire available history, including demographics and tacrolimus concentration.

3.7. Post-Transplant Phase Modeling

Studies can be categorized into three modeling approached according to how post-transplant phases are managed: phase-specific models [45,113] that are designed for a specific time window, temporal covariate unified models [40,122] to capture post-transplant trajectory, and stable-only models [12,102] that deliberately exclude early stages. None of the three categories are restricted to inpatient or outpatient settings. Tacrolimus CL/F undergoes substantial changes from immediate to stable post-operative periods due to hepatic regeneration and hematocrit recovery, which directly influences model selection.
The clinical utility of CYP3A5 genotyping is equally phase-dependent. High-dose corticosteroids early post-transplant pharmacologically increase CYP3A4 expression, masking genotypic differences [122]. Woillard et al. (2011) further observed that the dose-requirement advantage of CYP3A5 expressors disappears by 6–12 months once therapeutic drug monitoring has stabilized individual doses [130].
Collectively, these suggest that model selection and the relevance of specific covariates should therefore always be considered relative to the post-transplant phase for which a model was developed and validated.
Figure 5 summarizes modeling techniques over the past 30 years. ML approaches to modeling tacrolimus levels were described as early as 1999 [58] but then fell dormant. Coinciding with the rise of ML in general, 10 of 50 studies (20%) published after 2020 used ML. XGBoost [21,74,91,128,132,134,135,143] and Artificial Neural Networks (ANNs) [21,58,74,135] were the most commonly (4 studies each) explored ML methods (Figure 4C).

3.8. Predictive Covariates

Eighty-three studies explored significant predictors affecting tacrolimus. The CYP3A5 genotype appeared in 66 of these studies and ranked highest in covariate analyses, reflecting its central role in tacrolimus metabolism by CYP3A [18,51,54,64,67,74,84,107,122,144]. However, the significance of the CYP3A genotype varied by predictive target (Figure 6).
CYP3A5 expressers were consistently reported to require 1.2–2.2 times higher doses to achieve a target blood level. However, the clinical utility of CYP3A5 genotyping varied with the post-transplant timeframe. Of 52 studies examining CYP3A5 temporal significance, 22 studies found no significant benefit at any timepoint, 18 studies showed a sustained benefit beyond the first week post-transplant [39,40,43,50,54,78,81,84,89,96,102,107,119,135,137,144], while 12 reported diminishing predictive value after the initial post-transplant period [12,27,61,63,67,71,75,82,86,118,121,127]. Niioka et al. specifically demonstrated that CYP3A5 genotype utility was most pronounced after day 14 post-transplant [107]. Notably, Kirubakaran et al., 2023 [86], and Storset et al., 2022, found that once trough concentration history becomes available, phenotypical response data may supersede genomics for daily dose adjustments. In liver transplant recipients, the donor CYP3A5 genotype might be particularly important beyond the first 3 months as hepatic metabolism influences tacrolimus clearance [75,102].
For AUC prediction, recent trough levels and dose history became more predictive than genomics, suggesting that phenotypic response data encompass more pharmacokinetic information than the genotype alone.
Hematocrit (39 studies) consistently affected the clearance rate (CL/F) as tacrolimus mechanistically binds to red blood cells. Post-operative days (POD) followed (36 studies), representing the time-dependent recovery of hepatic enzyme activity. Weight (28 studies) consistently affected the volume of distribution (Vd). Demographics, including age (21 studies) and sex (11 studies), were significant, representing age- and sex-related metabolic changes, followed by serum albumin and serum creatinine (27 studies combined), representing hepatic and kidney function. Co-medication including azole antifungals (20 studies) was highlighted as a significant covariate, consistent with their role as CYP3A inhibitors.
Figure 7 summarizes the frequency of studies that incorporated each covariate in their final model.
The CYP3A5 * 1 allele in kidney and liver studies is reported to be the most clinically important, with effects ranging from 26% to an over 3-fold increase in CL/F depending on the population (Supplementary Material S6). This large variability likely suggests that model estimates are sensitive towards population compositions, time post-transplant, and how CYPS3A5 genotypes are split. Reséndiz-Galván et al. reported a 30% vs. 39% hematocrit, the second most frequent covariate, to result in approximately 8–10% higher CL/F, which reflects a mechanistic tacrolimus behavior of having fewer red blood cells, resulting in faster free drug clearance.

3.9. Model Performance, Calibration, and Error Handling

3.9.1. Performance Metrics

Performance metrics varied by modeling technique, with studies either assessing the performance in achieving target concentrations or evaluating the dosing accuracy in retrospective data. These metrics fell into three main categories: (1) bias/precision metrics indicating prediction error including median prediction error (MPE) and mean absolute prediction error (MAPE) (78 studies); (2) model fit metrics assessing correlation between predicted and observed values (R2, RMSE or root mean square error) (52 studies); and (3) clinical metrics (fraction within acceptable ranges (prediction errors within ±20% of the actual values or F20, and prediction errors within ±30% of the actual values or F30)) to evaluate target achievement and maintenance (29 studies). Complete definitions for these metrics are provided in Supplementary Material S4. Tables S10 and S11 in Supplementary Material S6 compare the error metrics between popPK and ML models for kidney and liver models.

3.9.2. Model Calibration

Model calibration (agreement between observed and predicted probability) was assessed through visual predictive checks (VPCs) in 42 studies and goodness-of-fit plots (GOF) in 58 studies. Notably, calibration at extreme values (very high or very low concentrations) was rarely explicitly studied, revealing a potentially important negligence of extreme concentration scenarios, where clinical consequences could be most severe.

3.9.3. Residual Error Handling

Residual errors between model-predicted and measured blood concentrations were reported in 92 studies. popPK models frequently (65 of 74 studies) reported residual errors. ML and regression methods (18 studies) relied on residual error-based regularization (L1/L2) to prevent overfitting (e.g., by tree pruning).

3.10. External Validation and Generalizability

Thirty-eight studies performed internal validation using bootstrapping. Only ten studies evaluated model performance on external data, showing limited transferability and generalizability within and across different organs, as these models performed poorly on external validation data [18,25,26,27,28,29,30,51,56].
The externally validated model development studies shared several distinguishing characteristics, including larger and more diverse development cohorts (e.g., Al-Kofahi et al. 2021: n = 608 development, n = 1361 external validation recipients), the CYP3A5 genotype and multi-covariate physiological frameworks within their covariate structures, and in some cases, prospective validation designs [51,71]. Their reported validation performance was, on balance, superior to internally validated models of a similar scale (Supplementary Material S6). However, standalone evaluation studies caution strongly against interpreting single-population external validation as evidence of broad generalizability. For instance, Methaneethorn et al., 2022 [101], found only 3 of 10 published models acceptable in a Thai kidney transplant cohort, and Kirubakaran et al., 2022 [19], found that all 17 evaluated models were systematically underpredicted in patients receiving concomitant azole antifungal therapy, regardless of the original validation status. Across external validation studies, prediction errors within ±30% of actual values (F30) were achieved in fewer than 50% of the predictions, with individual patient prediction errors ranging from 60% to ≥200% [18]. Zhao et al., 2016 [18], demonstrated that Bayesian priors can significantly boost performance in externally validated models, suggesting that incorporating prior population information may improve generalizability.

3.11. Interpretability

Interpretability, the extent to which humans can explain ML models’ decision-making, was limited to feature importance in three of the tree-based models [91,121,132]. We note an absence of commonly used interpretability tools in the literature, such as SHapley Additive exPlanation (SHAP) analysis and permutation feature importance (PFI).

3.12. Data and Modeling Availability

Eight studies indicated willingness to share their trained model upon request [95,98,114,115,116,117,119,141]. Three studies have source code available upon request [106,132,133]. Exceptionally, Loer et al., 2023, provided an open-access GitHub repository with full model implementation [95]. Mathematical descriptions for the popPK models were available within the manuscript for 102 studies.

3.13. Confidence in Evidence

The assessment of the quality of evidence using GRADE demonstrates a high certainty of evidence for analytical models of tacrolimus dose and concentration prediction, and identification of significant influencing factors on tacrolimus pharmacokinetics characteristics (Supplementary Material S5). Moderate certainty exists for AUC prediction due to concerns regarding patient population bias and lack of generalizability. Low certainty exists for pharmacokinetics parameter prediction studies due to the risk of bias and imprecision.

4. Discussion

This systematic review of 115 studies, aggregating different endpoints (AUC, trough, pharmacokinetic parameters, and dose predictions) and time windows, revealed that despite decades of modeling research, widespread clinical adoption of tacrolimus dosing models remains elusive. While popPK models dominate, ML approaches have become increasingly prevalent in the past 5 years (10 of 50 studies published since 2020). No studies employed RL, an approach well-suited for sequential decision-making, despite RL’s success in other therapeutic drug monitoring, such as warfarin (Patel et al.) [145].

4.1. Limited External Validation

A significant finding is the lack of external validation through clinical trials and meta-analysis. Despite Shi et al.’s clinical trial demonstrating the superiority of the model-based dosing over clinician dosing in achieving target therapeutic ranges, their small inpatient sample size inhibits generalization [14]. We found that meta-analysis of existing studies could not be completed due to the limited clinical validation, with different endpoints and limited sample sizes within each study.
Only ten studies reported external validation, raising generalizability concerns [18]. Zhao et al. evaluated 16 popPK (dose recommendation for kidney transplant recipients) and showed poor external predictability (F30 under 50%), with improvements when using Bayesian forecasting with 2–3 prior troughs [18]. This likely highlights that models capture training population-specific patterns rather than generalizable ones [18,56].
Among the externally validated development studies, shared characteristics, including larger development cohorts and multi-center populations, potentially contributed to superior transferability. However, standalone evaluation studies, e.g., Methaneethorn et al. [101] in a kidney cohort, or Kirubakaran et al. [19] in heart transplant recipients, demonstrated that external validation success in one population does not guarantee generalizable performance, highlighting that generalizability should be prospectively demonstrated.

4.2. Modeling Approaches

popPK modeling techniques are the most prevalent and validated, especially two-compartment models with Bayesian estimation, providing mechanistic insight into tacrolimus kinetics [122]. However, ML methods, especially XGBoost, NN, and hybrid popPK-ML models, have recently gained attention, showing competitive performance. ML approaches can handle high-dimensional, complex, nonlinear relationships without prior assumptions [21,135]. While ML models have been reported to have achieved accurate predictions (Zhang et al.’s TabNet [135] and Huo et al.’s LSTM [146]), these finding have not yet been replicated through external validation and therefore remain far from clinical use.
The head-to-head studies [121,132] compared PK to ML models, showing ML had incremental improvement over Bayesian estimation for dose prediction. Given the marginal improvements in accuracy reported for ML models over PK methods, the trade-off between interpretability and complexity should be considered. ML models demonstrated mechanistically meaningful covariates, which suggest that interpretability loss is marginal compared to the improved accuracy. Nevertheless, ML models incorporating PK models may benefit from both improved performance and interpretability.

4.3. Predictive Variables

Strong predictors include CYP3A5 genotypes, hematocrit, POD, and weight. Clinical utility of genetic testing faces significant challenges due to its limited availability and cost [147]. Despite CYP3A5 expressors requiring 1.2–2.2 times higher doses [78,81,82], the clinical impact of genomic testing might not be significant beyond initial dosing [9,148]. Recent studies, like that of Hue et al., achieved a strong predictive performance without genomics, suggesting that prior dose response data accounts for genomic and other variables sufficient to empower day-to-day dose adjustments beyond the first few days of tacrolimus initiation.
Several standard-of-care variables are consistently predictive. Hematocrit affects tacrolimus distribution, as tacrolimus binds to red blood cells [78] and patient weight influences Vd and CL/F [50,54,84,90,102,105]. However, clinicians often adapt individual dosing by accounting for additional factors, such as data collection issues (e.g., sample collection timing mismatch), patient adherence to instructions, social factors, the evolving patient health status, and foreseeable changes to the patient state. These nuanced factors are often only captured in unstructured data (e.g., clinical notes) and are therefore not leveraged by current modeling approaches. No studies incorporated clinical notes or adherence data, despite medication adherence being a known confounding determinant of tacrolimus variability and long-term graft survival [149,150]. For all modeling types, undetected non-adherence is a significant silent predictor, because, for instance, a model will interpret a subtherapeutic trough as requiring an increased dose, whereas the true issue is a missed or late prior dose. Future work could endeavor to quantify adherence in outpatient settings in structured fields using tracking apps or smart medication dispensers, or develop long-acting injectables that can be better controlled. Nevertheless, patient compliance is a well-recognized challenge in medicine that does not have simple solutions.

4.4. Outcomes

No studies predicted long-term clinical outcomes such as graft survival. Current models (90 studies) predict short-term targets such as the next-day concentration, whereas the ultimate goal of a transplant is long-term graft survival.
Model calibrations at extreme concentrations were limited [18,39,56,110,135], and the error was not stratified by subgroups [18,39,56,110,135]. While extreme values (demonstrating high-risk zones) represent a small fraction of the cases, these are where clinical consequences may be the most severe. Future work should weigh these extreme events more heavily or employ a priori limits to avoid unintended model predictions and consequences.
Current evaluation methods primarily rely on error-based metrics comparing predicted and observed values. When values are the prescribed dose, error-based metrics reflect the modeling of prescription patterns. For therapeutic drug monitoring in prospective studies, this approach also has limitations, as the target concentration is only a population estimate—not an exact patient-specific target. Alongside error-based metrics, more clinically meaningful evaluations, interventional prospective trials, and clinically relevant therapeutic-based metrics such as F20/F30 or time in the therapeutic range (TTR) [151] should be incorporated for model-based dosing methods. Likewise, in future prospective studies, patient outcomes such as symptoms, survival and quality of life should be considered. These outcome-based metrics should be incorporated alongside error metrics, to improve suboptimal clinical decisions as well as account for long-term transplant outcomes, especially in dose optimization models.

4.5. Suggestions for Future Research

Our findings underscore the importance of incorporating clinically relevant covariates in predictive models, including the retrospective dose response, hematocrit, body weight, and POD. Future research should transition to using more holistic evaluation methods to directly measure successful tacrolimus therapy delivery rather than comparing the model to the standard of care. Sequential modeling approaches, such as RL methods [152,153], should be explored to better account for the long-term clinical outcome of a transplant. Most importantly, this review found a lack of external validation and clinical translation. The absence of externally validated models is an important barrier to prospective clinical evaluation [32]. Future research should focus on comprehensive external validation, sequential decision-making modeling, and integrating other real-world clinical factors that influence dosing decisions, including those derived from non-structured clinical reports. To make ML models interpretable, future research should include interpretability tools such as SHAP or PFI when reporting modeling results. Finally, similar to the work of Loer et al., open-source code and implementation should be adopted as best practices in clinical data science and AI.

4.6. Limitations and Strengths of This Review

This review was limited to English and French studies. Furthermore, despite our intentions, ultimately, there were insufficient studies for a meta-analysis. However, we found a consistent pattern of increasingly complex modeling methods with no significantly demonstrated clinical benefits, largely due to a lack of external validation or clinical trials. This highlights study challenges rather than methodological limitations, which will require greater collaboration between clinics to overcome. Lastly, we used the JBI Appraisal Tool instead of PROBAST (Prediction model Risk of Bias ASsessment Tool) as we explored a variety of study designs for the prediction models.

5. Conclusions

Tacrolimus concentration predictions and dosing recommendations are commonly explored using population-based pharmacokinetic models, with recent ML approaches showing promise for incremental improvement. The field is currently limited by minimal demonstration of generalizability through external validation. Future models may benefit from incorporating underutilized data sources such as patient adherence, exploring sequential decision-making models like reinforcement learning, and modeling beyond the critical period of the first three months post-transplant to account for long-term transplant outcomes. Lastly, this field could benefit from reproducibility through the open sharing of data and models.
Ultimately, for clinical translation, modeling approaches should demonstrate a strong performance in multicenter clinical trials across different populations. To achieve this, there needs to be standardized external validation focused on the clinically relevant performance. Lastly, integration with electronic medical record systems is essential to enable efficient clinical implementation.

Supplementary Materials

The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/pharmaceutics18040430/s1, Supplementary Material S1 includes PRISMA checklist. Supplementary Material S2 includes the Medline search strategy. Supplementary Material S3 includes Table S1: Critical appraisal for non-randomized control trials, and Table S2: Critical appraisal for randomized control trials. Supplementary Material S4 includes Table S3. Definition of performance metrics used in the literature, Table S4: Model fit metrics, Table S5: Validation metrics, Table S6: Summary statistics, and Table S7. Meta analysis metrics. Supplementary Material S5 includes Table S8. GRADE certainty of evidence ratings. Supplementary Material S6 includes Table S9. CYP3A5 Genotype Effect on CL/F, the Most Dominant Covariate, Table S10. Machine Learning Models, Predictive Performance (Kidney and Liver Transplant). NR indicates that the metric was not reported (not that it was zero or not applicable), Table S11. Population Pharmacokinetic (popPK) Models’ Predictive Performance (Kidney and Liver Transplant). NR indicates that the metric was not reported (not that it was zero or not applicable), Table S12. External Validation Studies of Tacrolimus Population Pharmacokinetic Models. Model-Development Studies with External Validation (n = 7), Table S13. External Validation Studies of Tacrolimus Population Pharmacokinetic Models. Standalone External Evaluation Papers (n = 5).

Author Contributions

E.A. and R.K. contributed to the conception of the research question. E.A., N.B., A.B., M.M.K. and N.M.A. contributed to the development and implementation of search strategies, eligibility criteria, and methodology for data synthesis. E.A., A.B., C.R.M., J.R.G., B.R., H.A., M.M.K., S.H., A.A., G.L.H. and R.K. contributed to the drafting of the manuscript and provided approval for the final version of this manuscript. All authors have read and agreed to the published version of the manuscript.

Funding

This review is funded by the Ottawa Hospital Academic Medical Organization (TOHAMO) Innovation Fund and the Ottawa Hospital Division of Medicine ELEVATE grant.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding authors.

Acknowledgments

We acknowledge the OHRI1 librarian, Risa Shorr, who guided us in developing the search strategies. Risa Shorr contributed to extracting data from the databases.

Conflicts of Interest

The authors declare they have no competing interests. R.K. received revenue shares and is a consultant to Jubilant DraxImage Inc. for Rubidium-82 generators and elution systems. R.K. performs collaborative research and receives in-kind support from Hermes Medical Solutions. R.K. consults for Boston Scientific. The remaining authors of this manuscript have no conflicts of interest to disclose as described by the MDPI Pharmaceutics Journal.

Abbreviations

The following abbreviations are used in this manuscript:
%PRED20Percentage of measured blood levels predicted within ±20% interval
1CMTOne compartment
2CMTTwo compartments
AdaBoostAdaptive Boosting
ANNArtificial neural network
APE%Absolute prediction error
ASTAspartate aminotransferase
AUCArea under concentration curve
BARTBayesian additive regression tree
BEBayesian estimation
BiasMedian percentage predictive error
BRTBoosted regression tree
CatBoostCategorical Boosting
F20Prediction errors within ±20% of the actual values
F30Prediction errors within ±30% of the actual values
GBDTGradient boosted decision tree
GBMGradient boosting machine
GMFEsGeometric mean fold errors
GOFGoodness-of-fit plots
IF20%F20 of individual prediction error%
IF30%F30 of individual prediction error%
ImprecisionMedian absolute percentage predictive error
IPE%Individual prediction error%
KNNK-nearest neighbor
LASSOLeast Absolute Shrinkage and Selection operator regression
LightGBMLight Gradient Boosting Machine
LRLinear regression
LSSLimited sampling strategy
LSTMLong short-term memory
MAEMean absolute error
MAIPEMedian absolute individual prediction error%
MARSMultivariate adaptive regression spline
MEMean error
MIPE%Median individual prediction error%
MLMachine learning
MLPMultilayer perceptron regression
MLRMultiple linear regression
MPEMedian prediction error
MRDsMean relative deviations
MREMean relative error
MSEMean squared error
PBPKPhysiologically based pharmacokinetic
PEPrediction error
PKPharmacokinetics
PODPost-operative days
popPKPopulation pharmacokinetics
RFRandom forest
RLReinforcement learning
RMSERoot mean square error
RMSECVRoot-mean-squared error of cross-validation
RRRidge regression
RTRegression tree
SEStandard error
SVMSupport vector machine
SVRSupport vector regression
TabNetTabular network
TDMTherapeutic drug monitoring
TTRTime in therapeutic range
VPCVisual predictive check
XGBoostExtreme gradient boosting

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Figure 1. PRISMA flow diagram for study selection.
Figure 1. PRISMA flow diagram for study selection.
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Figure 2. Characteristics of the included studies (n = 115). Panel (A) shows the distribution of the transplanted organs studied, with 74 (64%) exploring kidney transplant recipients as their primary population, and “other” referring to multiorgan studies. Panel (B) shows different study methodologies, with the vast majority (88%) being retrospective in design. Panel (C) is a histogram of study population sizes, which ranged from 10 to 5439 patients. Panel (D) summarizes the post-transplant follow-up period of patients in each study. Panel (E) summarizes the tacrolimus formulations studied, with immediate release being the most common (56%). Panel (F) summarizes the tacrolimus blood concentration measurement methods used in each study, with immunoassay techniques being the most common (51%). Panel (G) is a histogram of the distribution of male percentage population across studies, with a median of 67% male population for model development. Panel (H) summarizes the number of studies with over 60% male population (n = 70) and one study with below a 40% male population.
Figure 2. Characteristics of the included studies (n = 115). Panel (A) shows the distribution of the transplanted organs studied, with 74 (64%) exploring kidney transplant recipients as their primary population, and “other” referring to multiorgan studies. Panel (B) shows different study methodologies, with the vast majority (88%) being retrospective in design. Panel (C) is a histogram of study population sizes, which ranged from 10 to 5439 patients. Panel (D) summarizes the post-transplant follow-up period of patients in each study. Panel (E) summarizes the tacrolimus formulations studied, with immediate release being the most common (56%). Panel (F) summarizes the tacrolimus blood concentration measurement methods used in each study, with immunoassay techniques being the most common (51%). Panel (G) is a histogram of the distribution of male percentage population across studies, with a median of 67% male population for model development. Panel (H) summarizes the number of studies with over 60% male population (n = 70) and one study with below a 40% male population.
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Figure 3. Frequency of study countries and their geographic distributions included in the review (n = 115).
Figure 3. Frequency of study countries and their geographic distributions included in the review (n = 115).
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Figure 4. Distribution of different modeling techniques. Panel (A) compares overall modeling approaches in reviewed studies (n = 115), with the most common approach (n = 74, 64%) being popPK modeling. Panel (B) compares different compartmental models, with 29 studies utilizing two-compartment models, followed by 23 utilizing one-compartment models. Panel (C) shows various ML approaches (XGBoost = Extreme Gradient Boosting, LASSO = Least Absolute Shrinkage and Selection Operator, SVM = Support Vector Machine, SVR = Support Vector Regression, KNN = K-Nearest Neighbor, MARS = Multivariate Adaptive Regression Spline, TabNet = Tabular Network, CatBoost = Categorical Boosting, AdaBoost = Adaptive Boosting, BART = Bayesian Additive Regression Trees, LightGBM = Light Gradient Boosting Machine, BRT= Boosted Regression Trees) explored, with Neural Networks and XGBoost being the most common. Panel (D) shows predicted target based on sampling strategies where hourly sampling is used in AUC prediction studies and pharmacokinetic parameter predictions, and daily sampling is used to trough or concentration prediction studies.
Figure 4. Distribution of different modeling techniques. Panel (A) compares overall modeling approaches in reviewed studies (n = 115), with the most common approach (n = 74, 64%) being popPK modeling. Panel (B) compares different compartmental models, with 29 studies utilizing two-compartment models, followed by 23 utilizing one-compartment models. Panel (C) shows various ML approaches (XGBoost = Extreme Gradient Boosting, LASSO = Least Absolute Shrinkage and Selection Operator, SVM = Support Vector Machine, SVR = Support Vector Regression, KNN = K-Nearest Neighbor, MARS = Multivariate Adaptive Regression Spline, TabNet = Tabular Network, CatBoost = Categorical Boosting, AdaBoost = Adaptive Boosting, BART = Bayesian Additive Regression Trees, LightGBM = Light Gradient Boosting Machine, BRT= Boosted Regression Trees) explored, with Neural Networks and XGBoost being the most common. Panel (D) shows predicted target based on sampling strategies where hourly sampling is used in AUC prediction studies and pharmacokinetic parameter predictions, and daily sampling is used to trough or concentration prediction studies.
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Figure 5. Trend of publications using different modeling techniques in recent years.
Figure 5. Trend of publications using different modeling techniques in recent years.
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Figure 6. The significance of CYP3A5 in different studies by target predictions. This figure summarizes CYP3A5 inclusion as a predictive covariate for different endpoints.
Figure 6. The significance of CYP3A5 in different studies by target predictions. This figure summarizes CYP3A5 inclusion as a predictive covariate for different endpoints.
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Figure 7. Frequency of different covariates and their categories used in final model development.
Figure 7. Frequency of different covariates and their categories used in final model development.
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Table 1. Single-compartment pharmacokinetic parameters’ definitions.
Table 1. Single-compartment pharmacokinetic parameters’ definitions.
Pharmacokinetic ParameterDefinition
Volume of Distribution (Vd)The theoretical volume into which the drug is distributed (e.g., plasma) [mL].
Elimination Rate (k)The relative rate at which the drug is removed from Vd [1/min]. The absolute elimination rate typically decreases with the concentration of the drug.
Half-life (t1/2)The time for the drug to decrease by half [min], and t1/2 = ln 2 k .
Clearance Rate (CL)The rate at which a volume is cleared of the drug CL = k·Vd = k/C [mL/min]. This rate is constant regardless of drug concentration.
Concentration (C)The amount of drug in the Vd [g/mL]. For most drugs, if we know the concentration in the blood at a certain time (C0), we can model the concentration at any future time (t) as C t = C 0 · e − k t .
Area Under the Curve (AUCx)The integral of the blood concentration over a finite time interval x. Because the concentration of tacrolimus changes with a t1/2 in the order of hours and dosing is once or twice daily, the AUC is a better clinical descriptor than a single concentration measurement. However, AUC measurements are not routinely viable, especially in the outpatient setting, as they require multiple blood draws between doses.
Table 2. Characteristics of the included studies. Gradient Boosted Decision Tree (GBDT), Random Forest (RF), support vector regression (SVR), K-nearest neighbor (KNN), Least Absolute Shrinkage and Selection Operator (LASSO) regression, ridge regression (RR), linear regression (LR), TabNet (Tabular Network), multiple linear regression (MLR), Limited Sampling Strategies (LSSs), Bayesian estimation (BE), multivariate linear regression (MLR), artificial neural network (ANN), regression tree (RT), multivariate adaptive regression splines (MARSs), boosted regression tree (BRT), Bayesian additive regression trees (BARTs), physiologically based pharmacokinetic (PBPK), multilayer perceptron regression (MLP), one-compartment (1CMT), two-compartment (2CMT), mean error (ME), mean absolute error (MAE), mean relative error (MRE), root mean squared error (RMSE), prediction error (PE%), absolute prediction error (APE%), individual PE% (IPE%), median IPE% (MIPE%), median absolute IPE% (MAIPE), F20 of IPE% (IF20%), F30 of IPE% (IF30%), standard error (SE%), %PRED20 (percentage of measured blood levels predicted within a 20% interval), mean relative deviations (MRDs), geometric mean fold errors (GMFEs), bias (median percentage predictive error), imprecision (median absolute percentage predictive error), root-mean-squared error of cross-validation (RMSECV), goodness-of-fit plots (GOF), visual predictive checks (VPCs), Therapeutic Drug Monitoring (TDM).
Table 2. Characteristics of the included studies. Gradient Boosted Decision Tree (GBDT), Random Forest (RF), support vector regression (SVR), K-nearest neighbor (KNN), Least Absolute Shrinkage and Selection Operator (LASSO) regression, ridge regression (RR), linear regression (LR), TabNet (Tabular Network), multiple linear regression (MLR), Limited Sampling Strategies (LSSs), Bayesian estimation (BE), multivariate linear regression (MLR), artificial neural network (ANN), regression tree (RT), multivariate adaptive regression splines (MARSs), boosted regression tree (BRT), Bayesian additive regression trees (BARTs), physiologically based pharmacokinetic (PBPK), multilayer perceptron regression (MLP), one-compartment (1CMT), two-compartment (2CMT), mean error (ME), mean absolute error (MAE), mean relative error (MRE), root mean squared error (RMSE), prediction error (PE%), absolute prediction error (APE%), individual PE% (IPE%), median IPE% (MIPE%), median absolute IPE% (MAIPE), F20 of IPE% (IF20%), F30 of IPE% (IF30%), standard error (SE%), %PRED20 (percentage of measured blood levels predicted within a 20% interval), mean relative deviations (MRDs), geometric mean fold errors (GMFEs), bias (median percentage predictive error), imprecision (median absolute percentage predictive error), root-mean-squared error of cross-validation (RMSECV), goodness-of-fit plots (GOF), visual predictive checks (VPCs), Therapeutic Drug Monitoring (TDM).
Primary Author, Publication YearSettingStudy MethodTransplant OrganTime Since TransplantSample Size [Dev/Val]Age
[Dev/Val]		%MaleModeling TechniquePredicted TargetOutcomePerformance Metrics
Abderahmene, 2024 [39]TunisiaRetrospective studyKidneyFirst 3 months337, 19656.25, 39.43 [Mean]6.53, 72.44popPK (2CMT with first-order absorption)Initial doseAccurate prediction of the target, found out CYP3A and age have a small effect on tacrolimus clearance in the validation cohort but significant differences between the two cohortsGOF, VPC
Al-fokahi, 2021 [40]USAMulti-center observationalKidneyVarying608, 136152, 5262.62popPKC/D prediction, significant predictorsGenotype significantly affects TAC pk; CYP3A5, CYP3A4, corticosteroids, calcium channel blocker and antiviral drug use, age, and diabetes significantly contributed to the CL/FME, MPE, RMSE
Allard, 2019 [41]FranceProspective multi-center randomized studyLiverDay 7 and day 9012, 1257, 59 [Median]83popPK (2CMT with linear elimination and a delayed first-order absorption with two transit compartments)PK parameters (early vs. late stages)Switching from Prograf to Advagraf in early stages could modify calcineurin activity (unrelated) to Tac Pk/PD; no statistical difference in trough in D90 and D104Diagnostic plots, GOF
Andreu, 2015 [42]The Netherlands Retrospective studyKidney<1 year16, 9156, - [Median]62.5popPK (2CMT), BE (LSS)C/D prediction, significant predictorsAccurate prediction of the target, popPK provides accurate prior information for MAP-Bayesian that predicts accurate AUCME, RMSE, bootstrap (200 runs), MPE%
Andreu, 2017 [43]SpainRetrospective studyKidney7–365 days304, 5952, 53 [Median]60.88popPK (2CMT with first-order absorption and a lag time), BESignificant predictors, initial doseAccurate prediction of the target (individual CL values); one-/two-/three-compartment models were tested; CYP3A5 and CYP3A, age, and hematocrit were significant predictors of TacMPE, RMSE, VPC, bootstrap (200 runs)
Andrews, 2019 [44]The NetherlandsRetrospective studyKidney<3 months337, 30456.95, 52 [Median]60.5, 65.8popPK (2CMT with first-order absorption)Initial doseHigher body surface area, lower creatinine, younger age, higher albumin and lower hematocrit also resulted in higher tacrolimus CL/F; starting dose should be increase by 160% in CYP3A5 carriers and reduced by 80% in non-carriersVPC
Antignac, 2005 [45]FranceRetrospective studyLiver11–66 days37, -52, - [Median]70.27popPK (1CMT with linear absorption and elimination), BESignificant predictorsVery low dose should be administered post Tx, dose can be increased once CL/F increases; Bayesian estimation performs best >15 days post-transplant and shows large interindividual variations in CL before thatGOF, bootstrap (1074 runs), RMSE
Antignac, 2011 [46]FranceRetrospective studyKidneyVarying33, -51, - [Mean]84.84popPK (1CMT with linear absorption and elimination), BETrough Bayesian method can predict concentration with a few of samplesME, MAE, RMSE
Åsberg, 2013 [12]NorwayRetrospective studyKidneyN/A69, 3041, 57 [Median]71popPK (3CMT with first-order absorption and lag time)Significant predictors, nest doseCYP3A5 genotype is influential and improves dose predictions and increases CL/F; CYP3A5 improves the predictions but the model does equally well when having 3–4 trough concentration in CYP3A5 absence PE, mean weighted PE, RMSE, R2, slope of the individual predicted versus observed plots
Barraclough, 2011 [27]AustraliaRetrospective studyKidneyVarying20, Jackknife49, - [Mean]60BE (LSS)AUC0-12Limited sampling method is better predictor than Bayesian method for C0 based on AUC0-12, C0 is poorly correlated with AUC0-12MPE, MPPE, RMSE, MAPE
Barraclough, 2012 [47]AustraliaRetrospective studyKidney10 patients: week 1, 10 patients: >3 months20, Jackknife49, - [Median]60MLR (LSS)AUC0-12Accurate prediction of the target using C0.5, C2, and C4 for early and late stages, these sampling times can be used for tacrolimus, mycophenolic acid and unbound prednisolone AUCJackknife, MPE, MPPE, RMSE, MAPE
Barraclough, 2022 [48]AustraliaMulti-center, prospective, observational studyKidney>1 month (<5 year)43, -53.6, - [Median]46.51popPK (2CMT with first-order absorption and a lag time), BESignificant predictorsThere is no difference in typical tacrolimus pharmacokinetics between Aboriginal and Caucasian recipients; greater between-patient variabilities in CL/F in AboriginalsOFV, GOF
BenFredj, 2016 [49]TunisiaRetrospective studyKidney≤3 months, 3–12 months, >12 months50, 2630.21, 33.25 [Mean]70PK (non-parametric adaptive grid approach)C0/D predictionAge, sex and weight do not significantly affect CL/F and Vd; showed there is a significant increase in C0/D within the first yearGOF, MPE, RMSE
Ben-Fredj, 2020 [50]TunisiaCross-sectionalKidney≥1 day77, 2533.5, - [Mean]68.6MLRC/D prediction, significant predictorsPOD, CYP3A4 and 5 are associated with C/D; sCYP3A4 is associated with lower Tac exposureR2, Bland–Altman
Ben-Fredj, 2023 [51]TunisiaProspective single-center studyKidneyN/A97, 7136.4, - [Mean]N/ABEC/D predictionModel cohort was nearly twice as likely to have C0 within the rangeR2, MAPE, RMSE, Bland–Altman
Benkali, 2009 [52]FranceRetrospective studyKidneyWeek 1 to month 632, Bootstrap (500 runs)54, - [Mean]59.3popPK (2CMT with Erlang absorption and 3 delay compartments), BEAUC0-12, significant predictorsAccurate prediction of the target using C0, C1 and C3; hematocrit and PXR genotype are covariates on CL/FBias, RMSE, comparing observe and predicted
Benkali, 2010 [53]FranceRetrospective studyKidney≥12 months29,1252, - [Median]46.34popPK 2CMT with Erlang absorption and 3 transit compartments, BE (LSS)pk parameters, AUC0-24Accurate prediction of the target using C0, C1, and C3; CYP3A5 is a significant covariate on CL/FBootstrap (1000 runs), VPC
Birdwell, 2012 [54]USARetrospective studyKidneyVarying446, -46, -61.4MLR, longitudinal data analysesC/D prediction, significant predictorsIncrease in albumin and weight found to be associated with decrease in C/D ratio while age increased it; model predictive accuracy increases in presence of genetic variantsN/A
Brooks, 2021 [30]AustraliaRetrospective studyKidney>1 month20, 052.5, - [Median]45BE (LSS)AUC0-12All 3 Bayesian forecasting programs/services evaluated had reasonable performance when using C0, C1, and C3MPE, MPPE, RMSE, MAPE
Cai, 2020 [55]ChinaRetrospective studyKidney≥3 months182, -37.9, - [Mean]74.7RFC/D prediction, next doseAccurate prediction of tacrolimus metabolism and dose requirements; CYP3A4 is more significant than CYP3A5 for TAC dispositionMDPE, MAPE, PE%
Cai, 2020 [56]ChinaRetrospective studyLiver4–50 days84, -51, - [Mean]82.1popPK (nonlinear Michaelis–Menten), BESignificant predictors, next dosepopPK MM outperformed linear one- and two-compartment models with first-order elimination meaning TAC pk are nonlinear; Bayesian form acting significantly improved predictionsRMSE, R2, RMSECV, the square correlation coefficients of cross-validation
Cai, 2022 [57]ChinaRetrospective studyLiver2–72 days176, -50.68, - [Mean]85popPK (1CMT with first-order absorption and elimination), nonlinear Michaelis–Menten (MM)pk parametersNonlinear MM was superior to the PK model and better described pk behavior; tacrolimus concentration to dose and metabolism may contribute to nonlinear behaviorGOF, MDPE%, MAE%
Catic-Dordevic, 2018 [28]SerbiaRetrospective studyKidneyN/A20, 1638.2, 40.6 [Mean]50Monte Carlo simulation (with respect to gender)AUC0-12Gender-specific sampling based on MC simulations are C1 and C8 post-dose for females and C8 for males prediction error (MAPE%)
Chen, 1999 [58]USARetrospective studyLiver<6 months10, 2246.13, 48.8 [Mean]68.75NN combined with Genetic AlgorithmTroughNN can predict whole-blood concentration but requires a large retrospective dataset to train onR, R2, Bootstrap (10,000 runs)
Chen, 2005 [59]ChinaRetrospective studyKidneyN/A16, -38.3, - [Mean]75Multiple stepwise regression analysisAUC0-12Accurate prediction of the target using C5, C1.5 (and C3); C5 might be the best single point to guide TAC dosePredicted vs. observed mean (+/− SD)
Chen, 2017 [60]ChinaRetrospective studyLiver>4 days125, -47.6, - [Mean]82.4popPK (2CMT with lag time), BE (LSS)Significant predictors, AUC0-12CYP3A, creatinine clearance and POD are found to be significant covariates of CL/F; AUC can include C0 and C2 (and C4); found that the best structural model for C0 is a 1-compartment model by the first-absorption process without lag time, and for full PK data, a two-compartment model by a single first-absorption process with lag timeR, R2
Chen, 2021 [61]ChinaRetrospective studyKidney0–90 days142, Bootstrap (1000 runs)40.9, - [Mean]67.6popPK (1CMT with the first-order absorption)Drug–drug interactionWuzhi capsule in low dosage exerts the optimum effect of tacrolimusGOF, bootstrap (1000 runs), VPCs, and normalized prediction distribution errors (NPDEs)
Choshi, 2024 [62]JapanRetrospective studyLungN/A119, 6N/AN/AMultivariate LSTM C0Dose, route and C0 are the most important variables in predicting future troughAccuracy, actual vs. predicted plot
Damon, 2017 [63]FranceRetrospective studyKidney10–90 days280, 189N/AN/APartial Least Squares regression multivariate predictiveSignificant predictors (Genomics)Up to 70% dose variability can be predicted by metabolism enzymes and transportersR2, SE, Bootstrap (1000 runs)
Dansirikul, 2004 [64]AustraliaRetrospective studyLiver11–1886 days31, Jack-knife47, - [Mean]74.19popPK (2CMT with first-order absorption and first-order elimination), noncompartmental model (LSS)AUC0-6, AUC0-12Best sampling times using regression equations were at C2, C4, and C5 rather than through; C5 is the most informative sampling time for AUC0-12R2, ME, RMSE, jackknife
Decrocq-Rudler, 2021 [65]FranceRetrospective studyLiver1–77 days55, 2455.2, 58.6 [Mean]63popPK (1 and 2CMT models
with first-order elimination), BE		Next doseAccurate prediction of the target using Bayesian forecastingMDPE, MDAPE, PE, F20, F30
Du, 2022 [66]ChinaRetrospective studyLiver2–538 days116, 2949.43, 51.3172.41popPK (1CMT with first-order absorption and elimination)Significant predictors, next dose Accurate prediction of the target, Wuzhi capsule, POD, eGFR, hemoglobin and albumin are associated with CL/F, and ALT and UREA are among the variables affecting V/FPE, MDPE, MAPE
Du, 2024 [67]ChinaRetrospective studyLungN/A210, -60, - [Median]79.5Linear regression analysisC/D prediction, significant predictorsFour SNPs are identified to be associated with Tac metabolism, accurate prediction of the initial dose using the modelMAPE, F20, F30
Du, 2024 [68]ChinaRetrospective studyLiver85.5–20 days31, (232, 57 concentration profiles)50.90, 50.84 [Mean]70.96ANNTroughAccurate prediction of the target; performs better than popPK models; daily dose, recipient age, recipient and donor CYP3A5 are significant influencers of TAC concentrationPE ± 30%, Bootstrap (1000 runs)
Elens, 2011 [69]BelgiumCross-sectionalKidney≥2 years99, -50.5, - [Mean]62Linear and logistic regressionSignificant predictorsCYP3A4 is more influential on tacrolimus metabolism than CYP3A5PE, mean prediction error (MPE) and mean absolute prediction error (MAE), R2
El-Nahhas, 2022 [70]UKRetrospective studyKidney>2 years15, 952.75, - [Mean]75Multiple linear regression (LSS)AUC0-24Accurate prediction of the target using C2 and C10 (and C0); LSS using C0 alone is suboptimalAIC, R2, ROC curve
Faelens, 2022 [71]BelgiumRetrospective studyKidney0–14 days315, -53, - [Median]63.4popPK (1CMT with oral absorption)Dose prediction (early stages)Improved dosing when using a model, no real improvement from a 2-CMT model or from the incorporation of available covariates (hematocrit)R2, Partial R2
Francke, 2022 [72]The NetherlandsProspective single-arm clinical trial studyKidneyVarying59, -59, - [Median]62.7BEInitial doseObserved vs. model-based did not differ significantly, with model-based dosing being slightly better, while model-based simulation showed lower interpatient variability and higher target achievements; a combination of an algorithm starting dose + model-based follow-up has potential to reduce adverse effectsPE, MPE%, MAE%, RMSE
Francke, 2022 [73]GermanyRetrospective studyKidneyN/A46, -65, - [Median]52popPK (2CMT with 1st-order absorption and lag time)PK prediction, doseBody composition is associated with tacrolimus pk and can improve its dose requirements; phase angle is positively correlated with TAC pkPE%, VPC, GOF
Fu, 2022 [74]ChinaRetrospective studyKidney1.5–20.5 days2040, 51139.72, 38.73 [Mean]64popPK, AdaBoost regressor, bagging regressor, DT, KNN, LASSO, MLP, SVR, RFNext doseExtra Trees Regressor accurately predicts the targetGOF, VPCs, bootstrap (1000 runs)
Gaies, 2013 [75]TunisiaRetrospective studyKidneyN/A20, Bootstrap (1000) and Jackknife31, - [Median]95popPK (2CMT with Erlang distribution to
describe the absorption phase and three delayed compartments), Bayesian estimation		AUC0-12Accurate prediction of the target using C0, C1 and C3PE, counts in therapeutic range
Gérard, 2014 [76]FranceOpen-label, non-comparative, prospective, observational studyLiver1–25 days66, -52.9, - [Mean]N/APBPK (13CMT)Initial dose Order of covariates that impact TAC C0: plasma unbound tacrolimus, typical intrinsic clearance, bioavailability, body weight, hematocrit, CYP3A5 polymorphism, proportion of fat, and CYP3A4 inhibitory drug–drug interactions; proposed C0 as a function of CYP3A5 donor genotype and patient’s hematocrit and body weight Percentage within 20% of actual dose, R2
Grover, 2011 [77]USARetrospective studyKidney7–53 months24, -52, - [Mean]63popPK (2CMT with first-order absorption and lag time), BE (LSS)pk parameters, significant predictorsNative Americans show lower clearance compared to whites; therefore, they may require lower doses to avoid toxicity OFV, GOF
Han, 2014 [78]Republic of KoreaRetrospective studyKidney≥2 weeks122, -41.9, - [Mean]54.91popPK (1CMT with first absorption and elimination and lag time), BETrough, significant predictorsCYP3A5 genotype and POD are significant predictors in early stages; CYP3A5 influences CL/F and POD decreases CL/FGOF, Bootstrap (2000 runs), VPC (1000 runs)
Han, 2019 [79]ChinaRetrospective studyHeart4–41 days107, 2451, 40 [Median]81popPK (1CMT with first-order absorption and elimination), BEC/D prediction, significant predictorsCYP3A5 genotype is influential and requires higher dose than nonexpressers; CL/F was significantly reduced in CYP3A5 nonexpressers, with Wuzhi capsules and with antifungal medsGOF; Bootstrap (1000 runs), VPC
Itohara, 2022 [80]JapanRetrospective studyKidney, Liver≥3 weeks18, - renal, 13, - liver51.2, - Kidney, 58, - Liver55.5, 53.8PBPK (15CMT)AUC0-12PK model derived in kidney transplant patients was applicable to liver transplant patientsPE%
Ji, 2018 [81]Republic of KoreaRetrospective studyLiver14 days58, -49.2, - [Mean]79popPK (1CMT with first-order absorption and elimination)pk parameters, next dosePOD and CYP3A5 affect CL/F in living donor recipientVPC
Jing, 2021 [82]ChinaRetrospective multi-center studyKidney>1 month165, -40.5, - [Mean]66popPK (1CMT with first-order absorption and elimination)Drug–drug interactionClearance rate of Tac decreases when combined with Wuzhi capsule; hematocrit, POD and CYP3A5 had significant influence on CL/FGOF, Bootstrap (1000 runs), VP
Kim, 2012 [83]Republic of KoreaRetrospective studyKidney0–12 months132, -38.6, - [Mean]59.84Linear mixed-effect modelingSignificant predictorsAge, body weight, hematocrit, serum creatinine levels, and CYP3A5 genotypes were found to be significant factors affecting trough; cadaveric transplantation is associated with increased risk of rejection95% CI
Kim, 2012 [84]Republic of KoreaRetrospective studyKidney1–5 years129, -38, - [Median]56.6Linear mixed-effect modeling, multivariate
Cox proportional hazards		Significant predictorsCYP3A5 is a variable marker for dose requirements, influencing factors vary depending on different post-transplant periods95% CI
Kim, 2019 [85]Republic of KoreaRetrospective studyKidney0.6–10.4 years32, Bootstrap (1000 runs)52, - [Median]63popPK (two-compartment with first-order absorption with lag time, and first-order elimination)pk parameters, significant predictorsCYP3A5 and MMF significantly affect TAC CL/F, effect of MMF on TAC exposure is more pronounced in CYP3A5 non-expressorsBias, imprecision
Kirubakaran, 2022 [19]AustraliaRetrospective studyHeart≤391 days85, -55, - [Median]67popPK (1 and 2CMT with first-order absorption—validating other models on this data)Next doseFailed to predict the target for the heart transplant recipients using popPK models developed from various solid organ transplant recipientsGOF, bias, imprecision
Kirubakaran, 2023 [86]AustraliaRetrospective studyHeartN/A47, 4053, 5667popPK (2CMT with first-order absorption), BE Significant predictors, PK parametersAccurate prediction of the target accounting for azole antifungal medication; concomitant azole antifungal therapy reduced tacrolimus CL/F by 80%; recent tacrolimus concentration is sufficient for predicting PK parametersBias, imprecision, Bootstrap (1000 runs)
Kirubakaran, 2024 [26]AustraliaRetrospective studyLung90 days43, -N/AN/ApopPK (various models), Bayesian estimationC/D prediction, significant predictorsModels developed for non-lung recipients perform poorly on lung cohort when concomitant antifungal therapy was present, but showed potential applicability in absence of concomitant antifungal therapyR2, Odds Ratio, 95% CI
Kuypers, 2004 [87]USAOpen-Label, retrospective studyKidneyN/A100, -51.4, - [Mean]59.12Multivariate logistic regressionSignificant predictors (in terms of rejection rates)Increasing serum albumin and hematocrit concentrations were associated with a prolonged concentration and contributed to lower risk of rejection; suggest shorter transit time of tacrolimus in certain tissue compartments, rather than failure to obtain a maximum absolute tacrolimus blood concentration, might lead to inadequate immunosuppression early after transplantationR2, MAPE%, MPE%
Langers, 2008 [88]The NetherlandsRetrospective studyLiver≥6 months23, -44.47, - [Mean]47popPK (2CMT with first-order absorption
without a lag time) (LSS)		AUC0-12Accurate prediction of the target using C4 and C6; C0 is not an accurate way of assessing systemic exposure for either formulationME, MAE, RMSE
Li, 2007 [89]ChinaRetrospective studyLiverVarying72, 3249, 51 [Median]86.53popPK (1CMT with first-order absorption and elimination)Significant predictors Total bilirubin and CYP3A in both donor and recipient are found to be significant variables on CL/FSE
Li, 2011 [90]ChinaRetrospective studyKidneyN/A142, -42.6, - [Mean]69.7Multiple stepwise linear regression analysisNext dose, significant predictorsAccurate prediction of the target, confirm CYP3A5, body weight, hematocrit, hemoglobin and total bilirubin significantly impact dose maintenancePE%, MPE, RMSE, F30%
Li, 2023 [91]ChinaRetrospective studyLiverN/A145, 3651, 51 [Median]85.63popPK (1CMT with first-order absorption and elimination), BE, XGBoostC0Combining popPK and XGBoost might improve trough prediction, XGBoost shows minimum MPE, popPK + ML can improve predictionsGOF, MPE, MAE, Bootstrap (2000 runs), normalized prediction distribution errors (NPDEs)
Ling, 2020 [92]ChinaRetrospective studyKidney0–30 days234, 1839, 40 [Median]69popPK (1CMT with first-order absorption and elimination)Significant predictorsCYP3A5 genotype, POD and hematocrit are significant predictors and affect CL/F in early stagesR2, PE, APE, MPE MAPE, Bland–Altman plot
Liu, 2020 [93]ChinaMulti-center retrospective studyLiver<6 months373, -51, - [Median]78MLRInitial dose, significant predictorsBoth donor and recipient CYP3A5 genotypes influence C/D ratio in early stages (3-month post) and donor is of primary importanceMPE), MAPE
Lloberas, 2023 [94]SpainProspective controlled, 2-arm, randomized, open-label, single-center trialKidneyDays 5, 10, 15, 30, 60, 9048, 4263.5, 63.5 [Median]73.3popPK Next dosePk-based dosing resulted in more significant TTR compared with the control groupResidual plots, Shapiro–Wilk test, IQR, p-value, ME, SE
Loer, 2023 [95]GermanyRetrospective studyVaryingVarying700, 30035, 35 [Mean]N/ApopPK Food/drug–drug interactionCYP3A4 is more influential on tacrolimus metabolism than CYP3A5GOF, MRDs, GMFEs
Macchi-Andanson, 2001 [96]ChinaRetrospective studyLiverFirst 2 weeks40, -48, - [Mean]72.5popPK (1CMT with first-order absorption, first-order elimination), BENext doseAs the model poorly predicted the target, it is suggested that trough levels are not proper predictors of individual dosingGOF plots, R, ME, RMSE, PRED20%
Marquet, 2018 [97]FranceMulti-center, prospective, randomized, open-label, parallel group studyKidneyDay 8, Day 9044, -51.8, - [Mean]75popPK (1CMT open with two gamma absorption laws), Bayesian estimation (LSS), MLRAUC0-24Similar exposure in both formulations, CYP3A5 explains ~31% of the variability in AUC, no influence of gender; AUC0-24 is more correlated with C24 than C0, AUC-to-trough level ratio was similar in both formulationsMean relative bias, RMSE, VPC
Marquet, 2021 [98]FranceMulti-center retrospective studyKidneyDay 7, month 1, and month 329, 759, 59 [Median]75.86popPK (1CMT with double gamma absorption, linear elimination), BE (LSS)AUC0-12Accurate prediction of the target using C0, C1 and C3, no need for CYP3A5 genotype for modeling AUCRMSE, Bland–Altman plots, number of differences out of the ± 20% acceptable range, R2
Mathew, 2008 [99]IndiaRetrospective studyKidney3–6 months29, Jack-knife32, - [Mean]82.75LSSAUC0-12Accurate prediction of the target using C0 and C1.5, which performed better than C0 and C4, marginal R2 improvement when more concentration samples addedPE%, APE%
Matsuda, 2022 [100]JapanRetrospective studyLungN/A20, -44.5, - [Median]55Linear mixed-effect modelingDrug–drug interactionC/D ratio increased by 2.25-fold when co-administered with itraconazole; CYP3A5 could contribute to interindividual variabilityGoF, AIC
Methaneethorn, 2022 [101]ThailandRetrospective studyKidney≥51 days74, -45.79, - [Mean]60.81popPK (2CMT first-order, Erlang
distribution, or transit compartment absorption), BE		Next doseAccurate prediction of the target using Bayesian post hoc estimationMAPE, RMSE, MSE, 95% CI
Moes, 2016 [102]The NetherlandsRetrospective studyLiverN/A66, Bootstrap (1000 runs)54, - [Mean]62.5LSS, popPK (2CMT with first-order elimination and h delayed absorption)Significant predictors, AUC0-24Accurate prediction of the target using 3 blood samples at C0, C2 and C3; age, weight, sex, hematocrit, hemoglobin, albumin, creatinine, BSA, BMI, LBW, co-medication, primary
diagnosis, and ethnicity are not significant on CL/F, V/F or K		95% CI, MPE, MAPE, and RSME, R2, Bootstrap (1000 runs)
Musuamba, 2009 [103]BelgiumRetrospective studyKidneyVarying19, -42, - [Median]84popPK (2CMT with first-order absorption and elimination)Significant predictorsTime of drug administration significantly impacts absorption rate constant, absorption rate varying in day vs. night administration, Circadian variation in tacrolimus absorption will not modify patient outcomesBIC, Bland–Altman analyses, RMSE, MRPE
Musuamba, 2013 [104]BelgiumRetrospective studyKidney0–1 month65, -N/AN/AMLR, BESignificant predictors, AUC0-12Age, co-medications and time post-transplantation are reported to be significant predictors, Bayesian estimator performed better than MLR, C1.5 and C3.5 showed best predictive performanceR2, RMSE, PE, Bland–Altman
Nanga, 2019 [105]FranceRetrospective study, systematic reviewKidney, liver, lung, and HCTVarying281, -2.3, - [Median]37popPK (2CMT with first-order absorption, absorption lag time and first-time varying elimination); external validationNext dose (early stages)Model validated across different age groups and organ transplants; post-operative time influences drug CL, whereas body weight influences Vd and CLDiagnosis scatter plots, VPC, bootstrap
Nguyen, 2023 [106]USARetrospective, cross-sectional, single center, open-label studyKidney≥6 months67, 1549.05, 57.2 [Mean]58.5popPK (2CMT model with first-order absorption and elimination with an absorption lag-time), BEAUC0-12Accurate prediction of the target; to improve predictions, there needs to be more longitudinal and biological data for modelingBland–Altman plots, rRMSE, rBias, R2
Niioka, 2015 [107]JapanRetrospective studyKidney0–30 days50, -50.5, - [Mean]68MLR, PK (non-compartmental)Significant predictorsCYP3A5 genotype is influential after day 14 post-transplantR2, Bias, SE, bootstrap
Op den Buijsch, 2007 [25]The NetherlandsRetrospective studyKidney>12 months37, -51.03, - [Mean]65Regression equation (limited sampling)AUC0-12Accurate prediction of the target, C0 and C12 have a lower predictive value for AUC0-12, LSS based on regression analysis is superior to LSS based on Bayesian fittingPE%, APE%, R2
Oteo, 2013 [108]SpainRetrospective studyLiver0–14 days75, -N/AN/ApopPK (1CMT with first-order absorption), BENext doseAccurate prediction of the target when combined with individualized biochemical assayMPE, RMSE
Pankewycz, 2020 [109]USARetrospective observational studyKidney≤12 months113, -49, - [Median]58Scoring formula (LSS) [TAC TDM × (MPA AUC + MPAG AUC/10)]Stable, over-/underexposure scoreScoring method accurately categorizes patients 6–12 months post-Tx into 3 categoriesROC analysis
Pei, 2023 [110]ChinaRetrospective studyHeart<1 month115, -52, - [Median]N/ApopPK (15CMT with first-order absorption)pk parametersAccurate prediction of the target; hematocrit should be considered as a significant influencer on C0 and AUC
Ragette, 2005 [111]GermanyRetrospective studyLung3–18 months15, -42.0, - [Mean]53Linear analysisAUC0-12Accurate prediction of the target using recommended C0/C4, C2/C4, and C0/C2/C4; using at least 2 or 3 concentrations between 0 and 4 h post-drug is required; true TAC exposure proved highly variable and a poor predictor of C0R2, 90% CI, fold error (predicted value/observed value)
Resendiz-Galvan, 2019 [112]MexicoRetrospective study (observational and mainly ambispective)Kidney4–2730 days52, 1336, 33 [Mean]61popPK (1CMT first-order conditional estimation method with interaction)Next dose, significant predictorsAccurate prediction of the target; hematocrit and CYP3A5 significantly affected CL/FAPE, R2
Riff, 2019 [113]FranceRetrospective studyLiverDay 7 and week 680, -41.5, --popPK (1CMT with first-order elimination and 2 γ-distributions), BEAUC and dose predictionAccurate prediction of the target using C0, C1 and C6 for Advagraf, C0, C2 and C6 for Prograf on Day 7 and C0, C1 and C3 in Week 6Observed versus individual predicted concentration plots, weighted residual error versus individual predicted concentration plots, visual predictive checks (VPCs) (1000), 90% prediction intervals
Rong, 2019 [114]CanadaRetrospective studyKidney<100 months49, -50, - [Mean]44.89popPK (1CMT with first-order absorption with a lag time, linear elimination, and constant error)Significant predictorsAccurate prediction of the target regardless of the post-transplant period; eGFR had significant effect on ClGoF, VPC, Bootstrap (500 runs), 95% CI
Saint-Marcoux, 2005 [115]FranceRetrospective studyLungN/A22, -40, -50popPK (1CMT with first-order elimination and double gamma absorption), BEAUC0-12Accurate prediction of the target using 3 blood samples at C0, C1 and C3 for non-cystic fibrosis (CF) and C0, C1.5, and C4 for CF patients Mean bias, RMSE
Saint-Marcoux, 2010 [116]FranceRetrospective studyKidneyDay 14 and Day 4212, -N/AN/ApopPK (1CMT with absorption described as following a double gamma distribution), BEAUC0-24Accurate prediction of the target using C0 and C0/doseObserved vs. estimated concentrations, Bayesian AUC0–24h estimates of LSS vs. linear trapezoidal rule applied to the full profiles (reference values), bias, RMSE
Saint-Marcoux, 2011 [29]FranceRetrospective studyKidney>12 months45, -N/AN/ApopPK (1CMT model with first-order elimination combined with a gamma model of absorption with 2 parallel absorption routes); BEDose prediction, AUC0-24Accurate prediction of the target; analytical method impacts the performance of Bayesian estimationMean bias +/− SD between observed and modeled concentrations, RMSE, squared correlation coefficients between observed and modeled concentrations, mean bias 6 SD between trapezoidal and Bayesian AUC0–24 h (extreme values)
Saint-Marcoux, 2013 [117]FranceMulti-center retrospective studyKidneyVarying100047.5, - [Mean]N/ARegression analysisAUC vs. C0C0 and AUC strongly linked in 1st 3 months after transplant; after 3 months, the relationship remained significant but was weakerPredicted vs. observed, R2
Scholten, 2005 [118]The NetherlandsRetrospective studyKidney2–52 weeks17, 2645.4, 46.9 [Mean]65popPK (2CMT with a lag time and first-order absorption)AUC0-12Accurate prediction of the target using C2 and C4R2, MPE%, MAPE%
Shi, 2023 [14]ChinaRetrospective study + multi-center, randomized, single-blind clinical trial studyLiver>28 days150, 79 (40 pilot trial)48, 50, [Median]82popPK (2CMT with first-order absorption)Next doseAccurate prediction of the target; model improved initial dose accuracy and reduced the number of adjustments, model-based doses were significantly individualizedScatter plot, ROC curve
Smith, 2023 [119]USAProspective studyKidney>12 months15, -N/AN/ABE vs. non-compartmental popPKAUC0-12MAP-Bayesian estimates the target using 9 sparse samples, comparable to NCA, which also uses 9 samplesRMSE, relative bias
Stifft, 2020 [120]FranceRetrospective studyKidney6 weeks and >6 months27, 2449, 55, unknown [Mean]56.86popPK (2CMT first-order absorption and elimination and with a lag time), LSS (MLR)AUC0-24Accurate prediction of the target using C8 via LSS (for early post-transplant)R, R2
Storas, 2022 [121]NorwayRetrospective studyKidneyVarying68, 755, 60 [Mean]77XGBoostAUC0-24Accurate prediction of the target using C2, C2.5, C3, C4, and C5MPE%, MAPE%, RMSE%
Storset, 2014 [122]Australia and NorwayRetrospective studyKidney≤21 days242, 7248, 53 [Mean]68popPK (2CMT with first-order absorption and a lag time)Significant predictorsAccurate prediction of the target using a theory-based popPK model rather than the empirical modelsRMSE, PE
Tang, 2017 [21]ChinaRetrospective studyKidneyN/A838, 20736.19, 35.82 [Mean]71.3MLR, ANN, RT, MARS, BRT, SVR, RF, LASSO, BARTNext doseAccurate prediction of the target using all the models, RT performed the bestMPE%, Bootstrap (10,000)
Tornatore, 2022 [13]USACross-sectional, open-label single centerKidney≥6 months65, -48.88, - [Mean]55.38popPK by multivariate linear regressionAUC0-12-to-adverse effects ratioAccurate prediction of the target; Black recipients showed higher AUC and Cl; greater adverse effects were found in women (and more in Black women)MAE%
Vadcharavivad, 2016 [123]ThailandRetrospective studyKidneyN/A96, -44.67, - [Mean] popPK (1CMT with first-order absorption)CL/F, V/FAccurate prediction of the target; hemoglobin and duration of TAC therapy could contribute to interindividual variabilitiesp-value
Valdivieso, 2013 [124]SpainRetrospective studyLiver0–15 days50, -N/AN/ApopPK (compartmental model with first-order conditional estimation method)Significant predictorsAccurate prediction of the target; low HCT and ALB contribute to TAC concentrationGoF, Bootstrap (1000 runs), VPC
vanBoekel, 2015 [125]The NetherlandsRetrospective studyKidney>6 months26, -43.9, - [Median]69LSSAUC0-24Accurate prediction of the target using C0, C2, and C4SEE%,
Velickovic-Radovanovic, 2010 [126]SerbiaRetrospective studyKidneyN/A18, -40.11, - [Mean]55Multiple stepwise regression analysisAUC0-12Accurate prediction of the target using C1.5, C4, and C8; women show significantly lower AUC valuesMPPE, MAPE
Velickovic-Radovanovic, 2015 [127]SerbiaProspective studyKidneyN/A20, 1638.2, 40.6 [Mean]50popPK (non-compartment)AUC0-12Gender-dependent pharmacokinetics in a steady state in terms of best sampling time in which measured Tac concentration best predicts AUC value (accurate prediction of the target using C2 in females and C1, C4 and C12 in males)R, R2
Wang, 2020 [128]ChinaRetrospective studyKidneyN/A406, -32.25, - [Median]73.89Regression TreeInitial dose, significant predictorsCYP3A5 and hemoglobin influence C0/D initial dosep-value, R
Wang, 2022 [129]ChinaRetrospective studyKidney3–215 days88 (65 PK, 23 LSS), -44, - [Mean]64.6Non-compartmental PK, BE and LSSAUC0-12Accurate prediction of the target using C4, C4, C6 and C10; patients with specific genotypes had higher AUC than the restPE, APE, MPE MAPE, R2, GoF
Woillard, 2011 [130]FranceRetrospective studyKidneyWeeks 1, 2 and months 1, 3, 6 and 1249, 2453.78, 53.78 [Mean]52popPK (2CMT with Erlang absorption (n = 3) and first-order elimination), and BEAUC0-12Accurate prediction of the target by Bayesian estimatorVPC, MPE, RMSE
Woillard, 2017 [131]FranceRetrospective studyKidney and liver≥6 months (0.5–14.25 years)73, 24 Kidney- 85, 28 liver50 (kidney), -; 52 (liver), -N/ApopPK (1CMT with first-order elimination and one or two absorption phases described by a sum of two gamma distributions), BEAUC0-24Accurate prediction of the target using C0, C1, and C3VPC
Woillard, 2021 [132]FranceRetrospective studyKidney, liver, heart, lung, other-2126, 70951.5, 51.5 [Median]N/AXGBoost (2 or 3 sampling times)AUC0-12, AUC0-24Accurate prediction of the target; XGBoost had superior performance compared with traditional PK modeling with Bayesian estimationRMSE, R2
Woillard, 2023 [133]FranceRetrospective studyKidney<3 and >12 months1325, -51, - [Median]N/APearson correlation or Bonferroni-corrected Tukey post-tests between AUC and C0C0AUC/C0 ratio is stable in large populations and can be used to estimate C0 in individualsR
Yoon, 2022 [134]Republic of KoreaRetrospective studyLiverN/A434, -N/AN/ALSTM and GBMInitial dose LSTM had better performanceRMSEMDPE, MDAPE
Zhang, 2022 [135]ChinaRetrospective studyKidney>3 months5439, -32, - [Median]69.8GBDT, RF, SVR, KNN, LASSO, RR, LR, and TabNetNext doseTabNet algorithm outperformed other algorithms with the highest R2R2, MAE, MSE, RMSE, and percentage of overestimated/underestimated dose in the testing cohort
Zhang, 2022 [136]ChinaRetrospective studyKidney≤21 days240, -39.4, - [Mean]73popPK (2CMT with first-order absorption and elimination)pk parametersAccurate prediction of the target in terms of Wuzhi capsule coadministration, 2-CMT model fit data better than 1-CMT modelMAE, MPE, F20%, F30%
Zhao, 2016 [18]ChinaRetrospective studyKidney3–90 days-, 52-, 38.9 [Mean]67popPK (1 and 2CMT, steady-state, and Michaelis–Menten), external validationNext dose, significant predictorsPublished models were unsatisfactory in prediction- and
simulation-based diagnostics, and thus inappropriate for direct
extrapolation correspondingly		PE%, MDPE, MDAE, F20, F30, VPC, IPE%, MIPE%, MAIPE%, IF20, and IF30
Zhu, 2013 [137]ChinaRetrospective studyLiverN/A26, -52.57, - [Mean]84.6LSSAUC0-12Accurate prediction of the target using C0 and C4PE%, APE%
Zhu, 2022 [138]ChinaRetrospective studyLiver51–150 days112, 2549, 50 [Median]74.45MLRSignificant predictors associated with C0/D11 metabolites (including microbiota-derived uremic retention solutes, bile acids, steroid hormones, and medium- and long-chain acylcarnitine) and clinical information found to be suitable predictorsR, ME, MAE, MRE, RMSE
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Amooei, E.; Biyani, N.; Buh, A.; Klamrowski, M.M.; Alyahya, N.M.; McCudden, C.R.; Green, J.R.; Rashidi, B.; Almuzirai, H.; Hoar, S.; et al. Analytical Models to Optimize Tacrolimus Dosing in Solid Organ Transplantation: A Systematic Review. Pharmaceutics 2026, 18, 430. https://doi.org/10.3390/pharmaceutics18040430

AMA Style

Amooei E, Biyani N, Buh A, Klamrowski MM, Alyahya NM, McCudden CR, Green JR, Rashidi B, Almuzirai H, Hoar S, et al. Analytical Models to Optimize Tacrolimus Dosing in Solid Organ Transplantation: A Systematic Review. Pharmaceutics. 2026; 18(4):430. https://doi.org/10.3390/pharmaceutics18040430

Chicago/Turabian Style

Amooei, Elmira, Nandini Biyani, Amos Buh, Martin M. Klamrowski, Nawaf M. Alyahya, Christopher R. McCudden, James R. Green, Babak Rashidi, Haya Almuzirai, Stephanie Hoar, and et al. 2026. "Analytical Models to Optimize Tacrolimus Dosing in Solid Organ Transplantation: A Systematic Review" Pharmaceutics 18, no. 4: 430. https://doi.org/10.3390/pharmaceutics18040430

APA Style

Amooei, E., Biyani, N., Buh, A., Klamrowski, M. M., Alyahya, N. M., McCudden, C. R., Green, J. R., Rashidi, B., Almuzirai, H., Hoar, S., Akbari, A., Hundemer, G. L., & Klein, R. (2026). Analytical Models to Optimize Tacrolimus Dosing in Solid Organ Transplantation: A Systematic Review. Pharmaceutics, 18(4), 430. https://doi.org/10.3390/pharmaceutics18040430

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